You CAN put a 500NE into a Gross Box action without it being a miserable, overweight junker. The question is why on earth would you want to do so? Answer: Because you bought a 577NE and you want a spare set of more-versatile 500NE barrels for your 577NE specialty gun.
The 470NE and 500NE are the same case, yet Heym doesn't even show the 470NE on the Gross Box in the brochure I'm looking at. Why? Because you'd be the proud owner of a 12.5lb 470NE...yuck.
The "standard" 470NE frame size from Heym is perfect, not only that it can handle 450-400, 450NE, 470NE, and 500NE, but also because it handles 20 gauge shotgun barrels which is a very handy thing to have when on safari for small antelope and wingshooting. (roughly $8000 for a set of shotgun barrels when ordering a new heym) The 375HH and Flanged barrels are also available on your big-bore 470NE frame, but they require very thick walls and are generally less than ideal, but it adds a lot of versatility.
Other members here have the smaller framed guns, such as VertigoBE's 7x65r smallbore Heym built on the petite action that accommodates his 375HH barrels ideally, with only a bit of excess weight and size on his 7mm barrels.
This is all sort of an academic discussion. 99.9% of buyers are going to buy a single barrel set for their Heym double rifle and they will buy the correct frame for that primary caliber. For those buying used Heyms, they're bargain shopping to get as much heym for the money as possible and as a consequence, you get what you get, free bonus barrels that are less than ideal but are offered on a used package basis for a fraction of their replacement cost.
Rough costs: Extra nitro caliber barrels on a new Heym = +$12,000. Extra shotgun barrels on a new Heym = +$8000.